Usually the web design company will take care of buying your domain name, but they may charge extra to do this, and it will need to be paid for every year or 2 so it could be worthwhile paying for it yourself. The domain name is of huge importance and should be something that you spend a lot of time considering. The web design company will be able to offer advice, but overall the choice will be down to you. If you have a company with a big brand name then you will probably want to have the name included in your domain. For example, if you have a gardening equipment company called Pitchfork then you will probably want the domain name pitchfork.com or something along those lines.